1. For electromagnetic wave propagation inside a good conductor, show that the electric and the magnetic fields are out of phase by 45⁰.

From the text, we see that the ratio of electric field to magnetic field is given by

For a good conductor, we can approximate this by .

2. A  2 kHz electromagnetic propagates in a  non-magnetic medium having a relative permittivity of 20 and a conductivity of 3.85 S/m. Determine if the material is a good conductor or otherwise. Calculate the phase velocity of the wave, the propagation and attenuation constants, the skin depth and the intrinsic impedance.

One can see that . The ratio of conductivity   to  is  which says it is r a good metal.  The propagation constant  and the attenuation constant  are given by,

The intrinsic impedance is

The phase velocity is .

The skin depth is

3. An electromagnetic wave with  its electric field perpendicular  to the plane of incidence is incident from vacuum onto the surface of a perfect conductor at an angle of incidence q. Obtain an expression for the total electric and the magnetic field.

The direction of electric and magnetic field for s polarization is as shown below.

Let the incident plane be y-z plane. The incident electric field is taken along the x direction and is given by

The minus sign comes because at z=0, for any y, the tangential component of the electric field must be zero.

The total electric field is along the x direction and is given by the sum of the above,

which is a travelling wave in the y direction but a standing wave in the z direction.  Since the wave propagates in vacuum, we have,

The magnetic field has both y and z components.